An important part of the well-known iterative closest point algorithm (ICP) is the variational problem. Several variants of the variational problem are known, such as point-to-point, point-to-plane, ...generalized ICP, and normal ICP (NICP). This paper proposes a closed-form exact solution for orthogonal registration of point clouds based on the generalized point-to-point ICP algorithm. We use points and normal vectors to align 3D point clouds, while the common point-to-point approach uses only the coordinates of points. The paper also presents a closed-form approximate solution to the variational problem of the NICP. In addition, the paper introduces a regularization approach and proposes reliable algorithms for solving variational problems using closed-form solutions. The performance of the algorithms is compared with that of common algorithms for solving variational problems of the ICP algorithm. The proposed paper is significantly extended version of Makovetskii et al. (CCIS 1090, 217–231, 2019).
Forensic gait analysis is used to visually and quantitatively analyze information regarding the appearance and style of walking that can be presented as evidence in the court. The demand for ...analyzing CCTV pedestrian footage in video surveillance has been increasing. The dependence of the accuracy of semiautomatic silhouette‐based analysis, often used in forensic science, on the differences in the viewing directions is a very challenging issue that is yet to be resolved for real case applications. Currently, the different viewing directions used in comparison footage significantly decrease the accuracy of same person analysis when using the silhouette‐based method, often used in the Japanese forensic science domain. A calibration‐based method was previously prosed to resolve this problem, but it requires performing an elaborate measurement procedure at the camera installation site for an accurate analysis. In this study, we propose a novel in‐silico silhouette‐based analysis method that significantly expands the number of viewing direction pre‐set settings to 900 from the 24 used in the previous method. Several software tools have been developed to ensure that all the procedures can be executed on a computer. The experimental results confirm that the accuracy of the proposed method is comparable to that of the calibration‐based method. Furthermore, the practical comparison results from actual consultation confirmed the effectiveness of the proposed method under existing viewing direction differences. We therefore anticipate that the proposed method will be beneficial for improving the analysis accuracy in real cases and therefore serve as a substitute of the previous method.
One of the fundamental issues in sensor networks is the coverage problem, which reflects how well a sensor network is monitored or tracked by sensors. In this paper, we formulate this problem as a ...decision problem, whose goal is to determine whether every point in the service area of the sensor network is covered by at least k sensors, where k is a given parameter. The sensing ranges of sensors can be unit disks or non-unit disks. We present polynomial-time algorithms, in terms of the number of sensors, that can be easily translated to distributed protocols. The result is a generalization of some earlier results where only k = 1 is assumed. Applications of the result include determining insufficiently covered areas in a sensor network, enhancing fault-tolerant capability in hostile regions, and conserving energies of redundant sensors in a randomly deployed network. Our solutions can be easily translated to distributed protocols to solve the coverage problem. PUBLICATION ABSTRACT
A planar maximum coverage location problem in a continuous formulation is considered. The demand zone and service areas are presented as geometric items of given shapes and sizes. Each service area ...is associated with a point (centroid), relative to which the corresponding geometric item forms. The task is to find the position of the centroids to provide an optimal service for the demand zone according to a given criterion. The mathematical model is constructed as a nonlinear optimization problem, in which the variables are the coordinates of the centroids, and the objective function is defined as the area of the demand zone covered by the services. For the formalization and calculation of the objective function, both analytical expressions and computer geometry software are used. The methodology we propose is applicable to the arbitrary shapes of both the demand zone and the service areas. Moreover, this technique does not depend on the complexity of the corresponding items, since it uses the Shapely library, which operates with the same Polygon class. An approach to solving the problem based on the consistent application of local and global optimization methods is proposed. An auxiliary problem is posed that allows one to significantly reduce the run time at the stage of local optimization. The implementation of the approach is illustrated by examples of the maximum coverage location problem when the demand zone is a polygon and the service areas have the shape of a circle and an ellipse. The innovation of this paper lies in the fact that the maximum service coverage problem in business site selection is studied in such a way that both the demand zone and the service areas have an arbitrary shape.
The registration of point clouds in a three-dimensional space is an important task in many areas of computer vision, including robotics and autonomous driving. The purpose of registration is to find ...a rigid geometric transformation to align two point clouds. The registration problem can be affected by noise and partiality (two point clouds only have a partial overlap). The Iterative Closed Point (ICP) algorithm is a common method for solving the registration problem. Recently, artificial neural networks have begun to be used in the registration of point clouds. The drawback of ICP and other registration algorithms is the possible convergence to a local minimum. Thus, an important characteristic of a registration algorithm is the ability to avoid local minima. In this paper, we propose an ICP-type registration algorithm (λ-ICP) that uses a multiparameter functional (λ-functional). The proposed λ-ICP algorithm generalizes the NICP algorithm (normal ICP). The application of the λ-functional requires a consistent choice of the eigenvectors of the covariance matrix of two point clouds. The paper also proposes an algorithm for choosing the directions of eigenvectors. The performance of the proposed λ-ICP algorithm is compared with that of a standard point-to-point ICP and neural network Deep Closest Points (DCP).
Abstract
In the study of origami, various parametric methods have been proposed to design crease patterns under geometric conditions for flat-folding. Each design method contributes to finding a ...desirable crease pattern, e.g., one with superior engineering properties, by manipulating parameters. On the other hand, to continuously deform other crease patterns, it is necessary to recreate it once with such a parametric method; however, this inverse problem is less studied. This paper is basic research to solve this problem and to allow parametric deformation of flat-foldable crease patterns. Given crease patterns are interpreted as networks consisting of twist-folding patterns that can be generated by an existing parametric method named twist-based design method. Then, by manipulating the parameters, the crease pattern is deformed. Importantly, any flat-foldable crease pattern having no crease line connecting two points on the boundary can be targeted, and it is locally guaranteed that deformed crease patterns have non-intersecting crease lines and are flat-foldable. The proposed method contributes to increased origami variations by deformations of existing crease patterns.
Graphical Abstract
Graphical Abstract
The relevance of this study is determined by complete absence of serious research in the use of flipped learning model (FLM) in teaching students of engineering universities Descriptive Geometry, ...Engineering and Computer Graphics, Computer Geometry (DGECGCG); by the absence of scientifically-based, tried and tested programs and teaching materials for flipped DGECGCG learning; as well as by the need for the development of new, modern tools to support classroom work and forms of students’ individual work. The purpose of the study is to examine the current state of knowledge and practice of existing DGECGCG courses, using the “flipped” concept as the main pedagogical strategy. Research methods of the issues were: pedagogical experiment, expert assessment (individual and collective) and cluster analysis (Euclidean distance, squared Euclidean distance, Ward’s clustering methods). The experiment involved 25 first-year students of Electromechanical and Mining faculties and 4 lecturers of the Department of Descriptive Geometry and Graphics of the Saint Petersburg Mining University. The results showed that since 2012, flipped learning has gained popularity not only among school teachers, but among professors of engineering universities. This article represents a synthesis of qualitative and quantitative researches of flipped learning models in the field of engineering education; students' attitude towards flipped learning, the role of teaching materials as well as the role of professor’s personality have been identified. Advantages and disadvantages of this learning model have been revealed. The study proved the absence of scientifically-based and tried and tested programs and instructional materials for teaching students DGECGCG using FLM. The need of further scientific researches of flipped DGECGCG learning models has been identified. Recommendations for training students have been provided. The materials of the article can be useful for Professors in the field of engineering.
Abstract
Origami tessellations are geometric pieces folded from a single sheet of paper with flatly overlapped facets. Most existing origami tessellations are constructed by first marking a grid of ...crease lines on the paper and then arranging repeating patterns along the grid. However, this design method is limited because it cannot design origami tessellations with patterns that cannot be represented on a grid, such as a regular pentagon. This paper proposes a new construction method for origami tessellations that solves this problem and enriches these varieties. In the proposed method, a boundary of an origami tessellation is determined first, and then patterns called triangle twist fold patterns are placed inside the boundary. A similar approach is known as a hole problem, although in this paper, the problem is redefined and discussed in a form suitable for origami tessellations. As a result, a grid-independent construction method was proposed, and new origami tessellations were obtained by using software that implements the method.
Graphical Abstract
Graphical Abstract
While wireless sensor networks (WSNs) are typically targeted at large-scale deployment, due to many practical or inevitable reasons, a WSN may not always remain connected. In this paper, we consider ...the possibility that a WSN may be spatially separated into multiple subnetworks. Data gathering, which is a fundamental mission of WSN, thus may rely on a mobile mule (ldquomulerdquo for short) to conduct data gathering by visiting each subnetwork. This leads to the problem of minimizing the path length traversed by the mobile mule. We show that minimizing the path length, which may reflect the data gathering latency and the energy consumption of the mule is a generalization of the traveling salesman problem and is NP-complete. Some heuristics based on geometrical properties of node deployment are proposed. Our simulation results show that these heuristics perform very close to optimal solutions in most practical cases.
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